Simulated viewpoint displacement apparatus



y 19, 1956 H. s. HEMSTREET 3,261,912

SIMULATED VIEWPOINT DISPLACEMENT APPARATUS Original Filed April 11, 19557 Sheets-Sheet 1 HAROLD S. HEMSTREET INVENTOR July 19, 1966 H. S.HEMSTREET SIMULATED VIEWPOINT DISPLACEMENT APPARATUS Original FiledApril 11, 1955 7 Sheets-Sheet 2 "1 Q N) ;l Q %4\ HAROLD S. HEMSTREETINVENTOR July 19, 1966 H. s. HEMSTREET SIMULATED VIEWPOINT DISPLACEMENTAPPARATUS Original Filed April 11, 1955 7 Sheets-Sheet 5 FIG 4 HAROLD S.HEMSTREET INVENTOR July 19, 1966 H. s. HEMSTREET SIMULATED VIEWPOINTDISPLACEMENT APPARATUS 7 Sheets-Sheet 5 Original Filed April 11, 1955HAROLD S. HEMSTREET INVENTOR ATTORNEY United States Patent Office3,251,912 Patented July 19, 1966 3 Claims. (Cl. 178-625) This inventionrelates to a simulated viewpoint displacement apparatus for producingimages having the appearance of areas as viewed from differentviewpoints and is a division of my copending application Serial No.241,098 filed November 6, 1962 which is a division of my prior copendingapplication Serial No. 500,325 filed April 11, 1955, now Patent No.3,101,645 issued August 27, 1963, which in turn is acontinuation-in-part of my copend-ing application Serial No. 480,033filed January 5, 1955 now Patent No. 2,999,322 issued September 12, 1961entitled Visual Display Method and Apparatus to which applicationsresort may be made as necessary, the present instant application showingan additional and improved means of providing simulated viewpointdisplacement. The copending applications illustrate in some detail theutilization of particular embodiments of the invention in conjunctionwith grounded training apparatus. The instant application, as well asthe disclosure of the previous applications shows apparatus and methodof considerable use in conjunction with grounded trainers, as well ashaving general utility in altering the apparent perspective of images.The previous applications concerned methods and means for distorting, oraltering the apparent perspective of images of areas as seen fromreference viewpoints so as to provide scenes such as would be viewedfrom points displaced from said reference viewpoints. One hereinillustrated form of the invention utilized for grounded aircrafttraining provides alteration of the apparent perspective of the imagesof objects such as frames of a motion picture film in accordance with asimulated flight path in order to provide a realistic display to astudent operating the grounded trainer. A motion picture may be made asa pilot flies a reference path, and then by providing controlled amountsof distortion of such picture in accordance with deviations of asimulated flight from such a reference path, a realistic visual displaymay be provided. The invention when used in conjunction with flighttraining apparatus also contemplates the provision of a plurality ofimages (such as motion picture films, for example) having the appearanceof areas as viewed at successive points along a reference path, and theprojection of such images to the operator of a grounded trainer withdistort-ion necessary to provide scenes having the same perspective asscenes such as would be viewed at points displaced from the referencepath.

The copending application illustrates the use of separate distortingmeans which independently distort an image, in one embodiment of saidinvention a variable magnification anamorphoser being provided todistort the image in accordance with vertical movement of the instantaneous viewpoint, and a rotatable prism or wedge being provided toaccomplish shear distortion, the sloping of an image in accordance withlateral movement of the instantaneous viewpoint. While the previousinvention is of great value in producing the desired image distortion,the amount of shear distortion attainable without prohibitive aberrationby means of the prism or wedge is sometimes undesirably limited insystems utilizing readily fabricated optical components, resulting in alimited range of allowable lateral displacement of the viewpoint. Theinvention provides improved method and means for accomplishing therequired vertical and shear distortion incident to provision from asingle image of scenes having the appearance of an area as viewed fromnumerous co-planer viewpoints, and cooperatively related distortingmeans are provided which produce the desired distortions in such amanner that increased ranges of displacement of the viewpoint may beallowed, and in which readily fabricated components are utilized. In oneembodiment of the present invention such improved distorting meanscomprise a pair of variable magnification anamorphic lens combinationshaving their axes of variable magnification acting in differentdirections, and in an illustrated preferred embodiment of the inventionsuch lens combinations act perpendicularly to each other to suitablydistort the image. In another embodiment of the present inventioncooperative electrical means are provided to distort the projected imagein required manner.

It is therefore a primary object of the invention to provide new andimproved means for altering the apparent perspective of images.

It is a further object of the invention to provide improved method andmeans for providing a visual display such as would be viewed from aselected viewpoint using objects having the appearance of an area asviewed from a viewpoint displaced from said selected viewpoint.

It is another object of the invention to provide improved method andmeans for providing visible displays of the type described which utilizecooperatively related means to alter the apparent perspective ofprojected images.

Other objects of the invention will in part be obvious and will in partappear hereinafter.

The invention accordingly comprises the several steps and the relationof one or more of such steps with respect to each of the others, and theapparatus embodying features of construction, combinations of elementsand arrangement of parts which are adapted to effect such steps, all asexemplified in the following detailed disclosure, and the scope of theinvention will be indicated in the claims.

For a fuller understanding of the nature and objects of the inventionreference should be had to the following detailed description taken inconnect-ion with the accompanying drawings, in which:

FIG. 1 is a perspective view of an exemplary form of grounded trainingapparatus adapted to use the invention, showing the general arrangementof such training apparatus;

FIGS. 2a and 2b are geometrical diagrams illustrating three differentshapes a rectangular grounded surface may present perspectively whenviewed from three dififerent viewpoints differing in altitude;

FIGS. 3a, 3b, and 3c are geometrical diagrams illustrating threedilferent shapes a rectangular grounded surface may presentperspectively when viewed from three laterally displaced viewpoints ofthe same altitude;

FIG. 4 is a geometrical diagram useful in illustrating the distortionrequired to simulate viewpoint displacement;

FIG. 5 is a geometrical diagram which taken in conjunction with FIG. 4is useful in understanding the propproperly the novel image distortingmeans of the invention;

FIG. 7 is a perspective drawing showing an exemplary form of opticaldistorting means constructed in accordance with the invention;

FIG. 8 is a geometrical diagram useful in understanding the occurrenceof an unwanted vertical shifting of the distorted image as an incidentto proper distortion of the image in some embodiments of the invention;

FIG. 9 is an electrical schematic diagram illustrating 'how theinvention may be interconnected with a conventional grounded aircrafttrainer to provide visual displays for use in grounded aircraftinstruction;

FIG. 10 is a perspective and cutaway view of a simple projector whichmay be used with the invention to project simulated sky area;

FIG. 11 is a perspective view of an exemplary form of tilting mechanismwhich may be used with the invention to rotate the projector so as toposition and align properly the distorted image on a viewing surface;

FIG. 12 is an electrical schematic diagram of an electrical distortingmeans constructed in accordance with the invention.

FIG. 13 is a geometrical diagram useful in understanding the operationof the film drive portion of the invention.

In all of the drawings like numerals refer to like parts.

FIG. 1 shows a specific arrangement of grounded training apparatusutilizing the invention for producing a visual display in conjunctionwith simulated aircraft flight. A mock-up of the cockpit of an actualaircraft is provided with dummy controls operable by a student pilot toprovide indications on simulated instruments and indicatorssubstantially duplicating those of an actual aircraft. The cockpit 10may also include conventional simulated radio signalling equipment (notshown) by means of which the student pilot may navigate. Situated nearthe cockpit is an instructors station which may include duplicatesimulated instruments, various controls 9, 9, for effecting special andemergency simulated flight conditions, and a conventional flight pathrecorder 11 to chart the ground track of simulated flight on a map 12.Grounded trainers commonly include a plurality of analogue computerswhich continuously solve the equations of motion of the simulatedaircraft, providing shaft outputs and electrical potentials to operatethe simulated instruments and indicators. Such computing apparatus maybe contained in cabinets 13. Grounded trainers which are primarilyintended for use in teaching instrument flying are usually provided withan opaque or translucent cockpit canopy, while in practice of theinvention there is provided a canopy 14 of glass, plexiglass orequivalent material substantially simulating the transparent windshieldof an aircraft. A plain white screen S is provided in front of thecockpit, the screen being preferably of a size suflicient to cover theentire area viewable by the student through canopy windshield 14. Lowambient light may be provided in the room in which the apparatus issituated, the intensity of such light being preferably that of a cloudyday. Cloud and lightning projectors known in the art may be utilized tosimulate flight under various weather conditions by projectingappropriate images and shadows onto canopy 13 or screen S. When theapparatus is utilized for teaching night flying, extremely low ambientlight may be provided to simulate night-time visibility conditions.

Cockpit 10 may be provided with arcuate rockers 15, 15 which are cradledupon rollers such as 17, 18 and similar rollers (not shown) on thestarboard side of the cockpit. Rigidly affixed to rocker 15 is a ringgear segment 19, which is driven through pinion 20 by cockpit rollservomotor M-700. Hence rotation of servomotor M-700 serves to rollcockpit 10 about an axis determined by the center of curvature ofrockers 15 and 16. Such center of curvature is preferably locatedsubstantially at the location of the eye of a student seated in thecockpit. Platform 21, upon which the cockpit and rolling mechanism iscarried, is provided with arcuate rockers such as 22 cradled betweenrollers such as 23. Ring gear segment or actuate rack 24 may be seenthrough the cutaway portion of platform 21 to be rigidly attached torocker 22 and meshed with pinion 25, so that rotation of cockpit pitchservomotor M800 rotates the cockpit about an axis determined by thecenter of curvature of rocker 22 and its counterpart (not shown) on thestarboard side of cockpit 10. Platform 26, which carries theabove-described pitching mechanism, is carried by vertical shaft 26,which is rotatably supported at its lower end (not shown) and which ischain-driven by means of cockpit turning servomotor M-900. The linethrough the centers of curvature of rocker 22 and its counterpart, andthe axis of vertical shaft 27 pass near or through the location of theeye of a student seated within the cockpit, so that cockpit pitching andturning motions occur about the students viewpoint. Thus as the studentviews a scene projected upon screen S, the cockpit may roll, pitch andyaw in a manner similar to that of an actual aircraft. Servos M-700,M-800 and M-900 may be driven by the same signals utilized inconventional grounded trainers for positioning roll, pitch and headingservos. If desired, proprioceptive effects may be simulated by operatingthe cockpit motion servos in accordance with the invention disclosed inapplication Serial No. 441,570 by Laurence E. Fogarty filed July 6,1954, for Grounded Aircraft Trainer, which application is assigned tothe same assignee as the present invention.

A motion picture projected upon screen S can be correct perspective-wisefor only one position of view, and that position of view preferablyshould not change as the cockpit is rotated. By rotating the cockpitabout axes coincident with the students eye, the correct viewpointperspective-wise may be maintained at the students eye. An actualaircraft rotates about its center of gravity, which seldom correspondsto the viewpoint of the pilot. In those systems in which the cockpit isrotated to cause simulation of proprioceptive effects such asseat-of-thepants reaction, it is usually desirable to rotate the cockpitabout a point corresponding to the aircraft center of gravity. Since theperspective distortion caused by displacing the axis of cockpit rotationfrom the students viewpoint is not serious in most embodiments of theinvention, it is sometime-s desirable to locate the axes of rotation ata compromise position between the students viewpoint and the cockpitsimulated center of gravity position.

Supported by column 42 a short distance above the cockpit and preferablyas near as possible to the eye of the student situated within thecockpit is a motion picture projector PR disposed to project an image ofa ground scene upon screen S for observation by the student. ProjectorPR may be mounted upon a tilting mechanism (indicated generally as 30)which allows rotation of the projector around three mutuallyperpendicular axes which coincide at the projection lens of projectorPR. As will be further explained below, distortion of the projectedimage by means of the pair of anamorphosers causes unwanted shifting androtation of the distorted image in some cases, and tilting mechanism 30serves to rotate projector PR so as to compensate for the undesiredshifting and rotation. A more detailed view of a specific tiltingmechanism is shown in FIG. 11. It will be apparent to those skilled inthe art that the precise form of tilting mechanism shown may be replacedby many other equivalent arrangements in practicing the invention.

Referring now in detail to FIG. 11 there is shown a pedestal 301 whichrotatably supports a yoke 302. The neck (not shown) of yoke 302comprises a shaft which is journalled in the upper portion of pedestal301 and which carries a bevel gear 303 at its extremity. Bevel pinion364 is driven by servomotor M-200, and being meshed with gear 303, yoke302 is rolled about a generally horizontal axis in accordance with theshaft rotation of servomotor M-200. Since projector PR is rotated byrotation of yoke 302, it will be seen that by suitable opera-tion ofservomotor M-200, the projected image may be rolled about an axisdefined by the axis of the neck of yoke 302. As will be furtherexplained below, servomotor M200 may be driven to rotate the projectedpicture by an (fi5 which will be the amount of rotation necessary tomaintain the horizon level on screen S as simulated viewpointdisplacement occurs.

The outer ends of the arms of yoke 302 carry shafts such as 305 uponwhich are rotatably carried a pair of hubs 306, 307 of a platformsupport. Depending from hubs 306 and 307 are arms such as 308, 309 and310 which carry pitching platform 311. Rigidly affixed to arm 308 andhub 306 is an arctuate gear segment 312 which meshes with pinion 313rotatably supported on the arm of yoke 302. Servomotor M-500 is rigidlymounted on yoke 302 and its output shaft is geared to drive pinion 313,thereby rotating platform 311 about the axis of hubs 306, 307. As willbe further explained below pitching of projector PR due to rotation ofservomotor M-500 will serve to move the projected image up or down onthe screen S to compensate for an unwanted Vertical shifting obtained asan incident to distorting the image. Projector PR is mounted upon acircular bearing plate 315 rotatably supported in platform 311 as shownby the cutaway detail at 316. A toothed portion of the periphery of theflange portion of plate 315 meshes with pinion 318. Servomotor M600 isrigidly mounted on platform 311 and its driving shaft rotates pinion318, thereby rotating projector PR about an axis defined by the centerof circular plate 315. Such rotation of projector PR serves to move theprojected image right or left on screen S to compensate for an unwantedlateral shifting obtained as an incident to distorting the image.Projector PR is in most respects a completely conventional motionpicture projector, having a few modifications which will be pointed outbelow. Mounted in front of the projection lens of projector PR is adistorting means which is shown in detail in FIG. 7. The three axes ofrotation of projector PR are mutually perpendicular and may be made tocoincide at the projection lens of projector PR. Such location of theaxes of rotation is not mandatory, but it serves to simplify theapparatus utilized to derive suitable operating potentials forservomotors M-200, M-500 and M-600.

Referring again to FIG. 1, there is shown a sky projector 330 fixedlymounted on column 42. Projector 330, which is shown in greater detail inFIG. serves to project an image of a blue or gray sky upon the upperportion of screen S. Projector 330 comprises a light source 331 shown ascomprising a conventional projection lamp, a collirnating lens 332, asky image plate 333 and a projection lens 334. The upper portion ofimage plate 333 may be blued or frosted While the lower portion isopaque. It will be apparent that such an arrangement will provide a blueor gray sky image having a horizon line defined by the boundary betweenthe opaque and translucent portions of plate 333. By varying theintensity of the voltage applied to lamp 331 the intensity of light inprojected sky scene may be varied. As will be apparent this may be donewith a simple rheostat (not shown).

As will be further explained below, the pictures which are projected maybe taken with the optical axis of the camera maintained upon thehorizon, in which case there will be no unwanted lateral or verticalshifting obtained as an incident to distorting the image. In suchapparatus servomotors M-500 and M-600 and their attendent mechanism maybe eliminated, and only the rotational correction supplied by servomotorM-200 need be provided. Maintaining the camera optical axis fixed on thehorizon results in pictures which are half sky, which is deemed a wasteof half of the field of the camera, since sky may be simulated easily bya simple projector such as that shown in FIG. 10, and it is desirable inmost cases to provide a display of as much ground area as possible.

Shown in FIG. 2a in heavy lines is a trapezoidal or keystone-shaped areaABCD such as the appearance in perspective a rectangular groundedsurface might have when viewed at a point situated at a particular placein line with the centerline YY of the area. From a position higher inaltitude than the initial viewpoint, the area might have an appearancesuch as trapezoid ABCD, and when viewed from a position lower inaltitude than the initial viewpoint, the area might have an appearancesuch as trapezoid A"B"C"D. In FIG. 2a line HH represents the horizon.

Shown in FIG. 2b is a side elevation view showing an eye situated atpoint P viewing a rectangular grounded surface at an altitude it abovesaid surface, the side BC of said surface being shown as a heavy line.It will be seen that if a screen S is placed a distance q in front ofviewpoint P, that a replica of the actual scene viewed from viewpoint Pmay be simulated by presentation of a proper scene on screen S. Assumingthat screen S is mounted in a generally vertical position as shown, itmap be seen that in order to effectuate a realistic presentation, thatthe distances of objects below the horizon on screen S must be inverselyproportional to the horizontal distance be tween those points and theground position of the viewpoint. For example, the distance h on screenS between the horizon and the simulated near end AB of the groundedsurface must be inversely proportional to R the horizontal distancebetween viewpoint P and the actual near end AB of the grounded surface,or as may be seen by similar triangles:

Similarly, the distance 11 on sceen S between the horizon and thesimulated far end CD of the grounded surface is inversely proportionalto R the horizontal distance between viewpoint P and the actual distanceto the far end of the surface, or that:

It may now be appreciated that for presentation of a scene such as thatseen above a grounded surface, that increases in viewpoint altituderequire proportionate increases in distances I1 and h of such scene, andthat con versely, decreases in viewpoint altitude require proportionatedecreases in distances h and I1 of such scene. Hence if a photographwere taken of a scene at a particular viewpoint, an appropriatestretching or squeezing of the image from such photograph with respectto the horizon would yield scenes such as those viewed at points aboveand below the point where the picture was taken.

Shown in FIG. 3 are appearances which a rectangular grounded surfacemight have when viewed from three viewpoints of the same altitude butvarying in lateral position with respect to the grounded surface. FIG.3b illustrates the scene which might beviewed from a viewpoint locatedon the centerline of the surface. FIG. 3a illustrates the same surfaceviewed from a viewpoint located a distance a to the right of thecenterline of the surface, and FIG. 30 illustrates the same surfaceviewed from a viewpoint located a distance b to the left of the centerline of the surface. Superimposed upon each of FIGS. 30!, 3b and 3c indashed lines is a rectangle representing a frame of a motion picture ora film which might be taken to project a simulated scene. It may be seenthat the displacements a and b of the centerline of the film at thelower edge of the film frame are proportional to the ratio of thelateral displacement of the viewpoint to the altitude of the viewpoint.If pictures were taken so that the hori zon in each picture is locatedalong the upper edge of the frame, then the lateral displacement of anypoint in the picture from its position in FIG. 3b is proportional to thedistance from the point to the top of the frame. Thus it may be seenthat by providing distortion of an image varying in accordance with themagnitude of lateral displacement from a reference viewpoint and varyinglinearly from zero distortion at a horizon point to maximum distortionat a nearest location, that scenes varying in accordance with lateraldisplacement of a viewpoint may be produced. Thus it may be understoodthat by stretching or squeezing an image of an area with respect to itshorizon or vanishing point, and by shearing the image linearly asdescribed above, images may be produced which have the appearance of thearea from various viewpoints. The distortion imposed as a result oflateral displacement of the viewpoint is termed shear distortion sinceit produces a shape similar to that produced by applying pure shearforces to an elastic member.

If the rectangle shown in FIG. 4 is a film frame or other object havingthe appearance of an area as viewed from a particular viewpoint, properstretching or squeezing of the image of the object and proper shearingof the image of the object in the manner described above will result inthe parallelogram image of FIG. 4, and the image produced by suchdistortion will represent the same area viewed from a differentviewpoint. The relationship between dimensions of scenes as viewed fromvarious viewpoints has been shown above, so that the required distortionto simulate a given change of viewpoint may be readily determined. Ihave discovered that a pair of perpendicularly-operating variableanamorphic elements may be utilized to provide the required distortions.For producing distortion to simulate a given viewpoint displacement,three relationships between the undistorted picture (rectangle) and thedistorted picture (parallelogram) may be determined: (1) the ratio ofheights, 11 to I1 (2) the angle a; and (3) the fact that the horizondimension (c in FIG. 4) remains constant. The three above conditions maybe utilized to determine three unknown conditions required to operatethe anamorphic distorting means; namely, the power of the first of theanamorphic elements, the power of the second of the anamorphic elements,and the angular rotation of the pair. By determining the three unknownquantities and instan taneously or continuously actuating the anamorphicpair in accordance with such quantities, the required distortion tosimulate a desired viewpoint displacement may be readily effected.

FIG. 5 is a geometrical diagram useful in understanding the ability of apair of crossed anamorphic elements to suitably distort an image. Thediagram shows a rectangle and a parallelogram, representing,respectively, an undistorted and a distored image of the same scene. MArepresents the axis of variably magnification of a first variableanamorphic element, and MB represents the axis of variable magnificationof the second variable anamorphic element. The anamorphic elements maybe positioned so that axes MA and MB are perpendicular to each other asshown in FIG. 5. The two anamorphic elements may be rotated together,and in FIG. 5 they are shown rotated an angle 8 about the system opticalaxis. The arrows along axis MA indicate that the image is compressedalong axis MA by a first anamorphic element having a magnification ofM,, along axis MA, and the arrows along axis MB indicate that the imageis expanded along axis MB by the second anamorphic element, which has apower of M along axis MB.

By trigonometry:

1 52 1 B =tan 5:521-

Since point D represents the same point relative to the distorted image(parallelogram) as point B is to the undistorted rectangle, it will beseen that line OB of the rectangle is expanded along axis MB by thesecond anamorphic element to a length OD, so that the relationshipbetween lines OB and OD may be expressed as:

Similarly, the relationship between lines 0C and 0A may be determined tobe:

OC=(0A)(M,,) By inspection,

Combining Equations (1), (2) and (3) and re-arranglng:

tan 6,:

L sl a M tan 6 (4) By similar process, the following expressions may bedetermined:

' tan 6 ]i I,, tan a (5) The height of the undistorted images may beseen to equal twice distance OE, or:

OE=h The height of the distorted image may be seen to equal twicedistance OH, or:

h OH By inspection:

OE 'cos B Since line 0G of the parallelogram corresponds to line OF ofthe rectangle modified by the magnification M, of the first anamorphicelement:

OG=M 0F (9) Combining Expressions (6) through (9):

l/Q cos B (10) Since angle JOG=, angle I OH may be seen to equal (905 sothat angle GOH equals 6 and therefore:

0H=OG cos 6 (11) cos B:

0=5 5 Applying Expression (14) to Expression (13):

cos B=MZOCSO? (15) By inspection of FIG. 4:

tan a= The six Equations (4), (5), (12), (14), (15), and (16) may beseen to contain six unknowns (13, M M a, 5 5 so that they may be solvedsimultaneously. The required values of anamorphic magnification M M andthe required rotation B of both anamorphosers to provide the distortedpicture desired may be determined.

Expressed in terms of sines and cosines and re-arranged, simultaneousExpressions (4), (5), (12), (14), (15), and (16) may be written asfollows:

M sin 6,, cos ,8=M cos 5,, sin ,3 (17) M sin 6 cos fi M cos 5 sin B (18)h M cos 6 =h cos [-3 (19) a= b M cos fi cos 0c cos B (21) h sin u=d cosa (22) The set of six simultaneous equations or equivalent expressionsmay be solved in accordance with well-known analogue computer techniqueas by provision of six servos, but the large number of interconnectingloops in such an arrangement requires in many embodiments of theinvention that extensive stabilizing be provided, and the complexity ofsuch an arrangement obviates ready analysis of its dynamic behavior. Itherefore prefer to solve individually for the required inputquantities, as will be further explained below.

If the film frames are taken with the optical axis of the cameramaintained toward the horizon, projection of the pictures through thedistortion means will provide the desired simulated viewpointdisplacement if the correct values of {3, M and M are provided, and ifthe entire optical system (including both the image and the distortingmeans) are rotated through the angle (FR-6 this rotation being necessaryto maintain the horizon level. If the frames are taken with thegopt-icalaxis of the camera pointed toward the horizon, much of the angular fieldof the optical system will be wasted unless it is deemed desirable toinclude large vamounts of sky in the picture. In producing visualdisplays for use in grounded aircraft training the simulation of sky maybe eifected very simply 'by other means, since sky area usually appearsthe same from all viewpoints. It is very desirable to utilize as much ofthe angular field of the optical system as possible for providing adisplay of grounded area, and hence it becomes desirable to take thefilm frames with the camera optical axis pointed Well below the horizon.This will require shifting of the projected image both laterally andvertically, as will be further explained below.

Referring to FIG. 8 assume that the eye of am ohserver is located atpoint P an altitude I2 (measured slant-wise as shown) above the ground.The area between the honizon and point B on the ground will be seen witha height I1 If a projected image of a film in plane F-F taken from pointP is cast onto screen S with a height I1 it will be seen that a faithfulreplica of the actual scene may be observed. If it be assumed that thefilm were taken and projected with the camera and projector optical axeslying along line PB at an angle of e to the horizontal, it will beappreciated that the portion of the picture projected along line PB willnot he displaced laterally or vertically. If simulation of an increasein viewpoint altitude (to an altitude of h above the ground) is to beeffected, it will be appreciated that as well as the picture beingexpanded to a new height h the undeviated axial portion of the picturemust be redirected downwardly so as to lie along line PB, providing animage having a height and location shown as It in FIG. 8. This may beaccomplished by shifting the plane of the film downwardly (upwardly inprojectors which invert the image) in the projector or by rotating theentire projector clockwise as viewed in FIG. 8. From inspection of FIG.8, it may be seen that:

l q tan 6 so that the required shift of the film vertically in plane FFwould equal:

ptane 10 where p is the focal length of the projection lens system, or,assuming that the tangent equals the angle for small angles of rotation,the entire projector may be rotated about a horizontal axis in its lensplane through the angle:

Since the film images are projected and distorted with reference tovertical and horizontal movement of the viewpoint within the [filmplane, it will be appreciated that the altitudes should be measuredparallel to the film plane F- F, so that reference altitude il of eachfilm frame is actually the altitude at which the picture was takendivided by the cosine of the projection angle 6. Since all film framesmay be taken and projected at the same angle with respect'to thehorizontal, cos 6 may remain constant, allowing the reference altitudeof each film frame to be constant regardless of viewpoint displacement.By analysis similar to that above, it may be seen that if the opticalaxes of the camera and projector are not located along the horizon line,that the distorted image must be shifted laterally also, which may beaccomplished either by lateral shift of the film itself in its own planein accordance with tan 6- P hz or by rotation of the projector about avertical line through its projection lens in accordance with d tan 6 Inorder to avoid mechanical complication of the projector shutter and filmfeed mechanism incident to shifting the film within the projector, Iprefer to effect the above-mentioned vertical and lateral shifting byrotating the projector and thusly positioning the distorted image on theviewing screen. Oompu ter apparatus connected so as to provide shaftoutputs suitable for rotating the projector to provide the requiredamounts of vertical and lateral shift is shown and explained in FIG. 6.

Equations (17) through (22) also may he solved analytically, and thefollowing expressions may be ohtained for M or the ratio between thepowers of the two variable anamorphic means:

The signs in expression (23) result from arbitrarily assuming that M MIt will be apparent that M and M may be interchanged by rotating boththe anamorphic means with respect to the image to be distorted. SinceEquation (23) is expressed in terms I1 hi and d, known quantities fordistortion required to simulate known movement of the viewpoint, it willbe seen that solution of the equation for given values of M willindicate the locus of viewpoints which may be simulated with a givenratio of anamorphoser powers. Re-arrangement of Equation (23) to thefollowing form indicates that each value of anamorphic pair power ratioM will provide displacement of the viewpoint in a circle centered at ad=0 point:

Solving the simultaneous equations analytically, one also may obtain anequation for the angle ,8 in terms of the anamorphic power ratio:

sin 25:

Equation (27) indicates that the paths of viewpoints simulated byconstant values of M are a system of hyper bolas, and Equation (28)indicates that the paths of viewpoints simulated by constant values of-M are ellipses.

In similar fashion the following expression may be obtained to describethe loci of viewpoints using a constant Expression (29) indicates thatthe loci of viewpoints obtained using a constant angle 13 are a familyof circles which pass through the 11 point.

The following expression for the angle (,86 through which the distortedimage must be rotated in order to maintain the horizon line in the sameplace also may be obtained:

d can (l35 -m 01, 1+ 2) sin (B cos (B b) As an alternative to theabovementioned computer simultaneously solving Equations (17) through(22), I prefer to build separate computers which solve for their ownindividual quantity from input data applied in terms of the knownviewpoint displacement quantities I1 I2 and d, as by means of servosolution of Expressions (27), (28), (29), and (30), or modified forms ofthese expressions. It may be noted that Expressions (27), (28), and (29)are each quartic equations making four solutions of each equationmathematically possible, and hence it is necessary that the computers beconnected so that the correct solution is always selected, as will befurther explained below.

Equation (27 may be re-arranged to the following Equation (28) may bere-arranged to the following Equation (29) may be reduced andre-arranged to the following form:

Shown in FIG. 6 in electrical schematic form is computing apparatuswhich solves Equations (30), (31), (32) and (33) to provide shaftoutputs to actuate the novel distorting apparatus of the invention so asto provide simulated viewpoint displacement for use with a conventionalgrounded aircraft trainer. Well-known analogue computer apparatus isshown in block form, and certain parts which would ordinarily be used inconstructing commercially acceptable apparatus are omitted for sake ofclarity. For example, in the construction of analogue computers bufferamplifiers are often used in numerous parts of a system to preventloading errors and to affect scaling of the computing potentials andother amplifiers are used solely for polarity inversion. Each of theservomechanisms shown may comprise conventional grounded trainerservomechanisms, and each may include a tachometer generator or otherrate feedback device for stabilization and anti-hunt purposes. Eitheralternating current or direct current computation may be used, and thealterations of the apparatus to convert from one system to the otherwill be readily apparent to those skilled in the art. Mechanical andelectrical limit switches ordinarily utilized to prevent overtravel ofvarious parts of the apparatus have been omitted for sake of clarity.Reduction gearing between the servomotors and driven apparatus has notbeen shown. Shown in block form and indicated as M-ltltltl is aconventional grounded trainer servomechanism which is positioned as willbe shown in FIG. 9 and which provides a shaft position according to thealtitude I2 of the reference viewpoint, which in systems utilizing filmimages will constitute the instantaneous effective altitude at whicheach film frame was exposed, divided by a constant, the cosine of theprojection angle 6, as discussed with FIG. 8. The reference altitude I1may be termed the effective altitude at which the picture was takensince the picture need not necessarily have been actually taken at thataltitude. In providing films for use with the apparatus described,anamorphosers may be utilized on the camera to provide films having theappearance of being taken from viewpoints displaced from the actualcamera location, or, anamorphosers may be utilized on the film printerto insert a variation in apparent perspective between the camera filmand the projector film. Shown as M-1100 is a conventional groundedtrainer altitude servo which provides an output shaft positioncommensurate with I1 the instantaneous altitude h of simulated flight,also divided by a constant cos 6. The constant cos 6 may be effected byresistance scaling. The invention will operate to distort the image ofeach film frame taken at its 11 altitude to provide a scene such aswould be seen at the I1 altitude then being flown by the groundedtrainer. Shown in block form as M4200 is a lateral displacement servoM-1200 which is positioned in accordance with deviation of the path ofsimulated flight from a reference path :as will be shown in FIG. 4 andwhich continuously provides an output shaft position commensurate withthe lateral displacement a in the viewpoint plane between the point atwhich the film frame being projected was taken and the simulatedaircraft position.

A constant potential from the computer power supply is applied to excitethe winding of potentiometer R-601, the arm of which is positioned bythe 11 servo M-1000, applying a potential proportional to I1 to excitepotentiometer 12-602, the arm of which is also positioned by servoM-1000, thereby deriving a potential commensurate with I2 on the arm ofpotentiometer R-602. As will be apparent to those skilled in the art,linear function otentiometers R-601 and R-602 may be replaced by asingle square function potentiometer if desired. The 11, potential onthe arm of potentiometer R-602 is applied through feedback amplifierU604 and resistance R-619 to the input circuit of feedback summingamplifier U-605, amplifier U-604 serving to reverse the polarity of thepotential. Potentiometer R-607 is excited by a constant supply potentialand its arm is positioned by the simulator altitude servo M4100, therebyapplying an I1 potential to potentiometer R-608, the arm of which isalso positioned by servo M-1100, thusly deriving an I1 potential on thearm of potentiometer R-608. The I1 potential is In FIGS. 6, 9 and 12certain applied via resistance R620 to the input circuit of summingamplifier U605. A a! potential is derived in similar manner and appliedto the input circuit of amplifier U-605 via summing resistance R-621.Summing amplifier U-605 combines the input potentials applied viaresistors R-619, R-620 and R-621, providing an output potentialcommensurate with h h -d This potential is applied directly and throughpolarity inversion amplifier U-613 to excite opposite ends of sinepotentiometer R-626. Potentiometer R-603 is excited with a lateraldisplacement voltage d from potentiometer R-611, and since the arm ofpotentiometer R603 is positioned by h servo M4000, a potentialcommensurate with 2dh may be applied to excite the'winding of cosinepotentiometer R-625. Those skilled in the art will recognize that theconstant multiplier 2 may be elfected by appropriate resistance scaling.Servo M-100 positions itself in accordance with the angle 2,6 by solvingEquation (33), the first term of the equation being applied to summingamplifier U-608 and the servomechanism via resistor R-636, and thesecond term being applied via resistor R635. As will be apparent, servoM-100 will run until the two applied inputs cancel each other, at whichtime its shaft position will be proportional to the angle 28. As shownin FIG. 7, servomotor M-100 drives gear 107 and angularly positions theanamorphic distorting pair in accordance with the angle 5, the factor oftwo being effected by the gear ratio. Rather than by solving Equation(30) as shown in FIG. 6, the B shaft position may be derived by solutionof equations such as expression (29), but the use of Expression (29) isdeemed preferably because the sine and cosine terms may be derivedeasily using readily available analogue computer resolvers. The systemof either equation however, may yield either of two answers. Byproviding the proper polarity excitation to B servomotor M-100 thedesired root may be selected. Reversing the polarity of such excitationwill cause servo M-100 to rotate 28 through 180 (i.e. ,8 thru 90) toselect the other root.

As seen in FIG. 6 potentials commensurate with i1 I1 and d are appliedfrom potentiometers R-602, R-608 and R612, respectively, throughresistances R-615, R 616 and R-618 respectively to the input circuit offeedback amplifier U-603. The output potential from amplifier U-603 isapplied to excite square function potentiometer R-604, the arm of whichis positioned in accordance with reference altitude h by servo M-1000,and the potential on the arm of potentiometer R-604 being applied viaresistor R-617 to the input circuit of amplifier U-603. As will bereadily apparent to those skilled in the art, such cnnection modifiesthe output potential of amplifier U-603 so as to provide an outputproportional to (I1 h +d divided by I1 This output potential, which maybe seen to equal the first bracketed quantities in Equations (31) and(32) is applied to excite square function otentiometers R631 and R634.The arm ofi square function potentiometer R-631 is positioned inaccordance with M the required magnification of the first anamorphicelement, by servo M-300, which solves Equation (31), applying apotential commensurate with the second term of Equation (31) to theinput circuit of the servo via summing resistor R639 and summingamplifier U-610. A constant potential from the computer power supplyexcites the winding of square function potentiometer R-629, and the Moutput is applied to excite square function potentiometer R630, thuslyderiving an M; potential for application to servo M-300 via summingresistor R-640 and amplifier U-610. To provide the third term ofEquation (31) the h} potential from potentiometer R-608 is applied viaresistor R-647 as one input to amplifier U-615. The output of amplifierU-615 excites square function potentiometer R-643, which is positionedby servo M1000, and the potential on the arm of potentiometer R-643 isapplied via resistor R4546 to a 1'4- amplifier U-615, providing anoutput potential from U-615 proportional to This potential as appliedvia summing resistor R-644 to amplifier U-610 and via summing resistorR-645 to amplifier U-611. Hence servos M-300 and M-400 are sup pliedwith input quantities in accordance with Equations (31) and (32), and bycontinuously solving the equations, shaft positions proportional to therequired anamorphic magnifications are provided. As shown in FIG. 7,servos M-300 and M400 vary the magnifications of the anamorphic pair byaxially positioning lenses.

Servos M300 and M400 may comprise identical servomechanisms, except thattheir quadrature excitations are of opposite polarity. Although thereare four possible solutions of the quartic equation solved, the servosmay be prevented by conventional mechanical limits (not shown) fromseeking negative power solutions, and by providing the proper directionof operation for a given polarity input signal, the servos will eachposition themselves to the desired roots. As is well known in theanalogue computer art, reversing the direction of operation of a servofor a given polarity input will cause a servo connected to solve aquadratic equation to seek the other root.

A constant potential from the computer power supply is applied to excitethe winding of potentiometer R-606, the arm of which is positioned byservo M4000, applying an h potential to amplifier U-607 via resistorR-623. Similarly, an h potential is derived by potentiometer R- 610 andapplied via resistor R-624 to amplifier U607. The output from amplifierU607 is applied both directly and through amplifier U-614 to exciteopposite terminals of sine potentiometer R-628. The potentialproportional.

to lateral displacement d from potentiometer R-611 is inverted inpolarity by amplifier U-612 and applied to excite the winding of cosinepotentiometer R627. Servo M-200 provides an output shaft positioncommensurate with the angle (/86 so that a (h -i-h sine (ii-6 potentialis applied to amplifier U-609 via resistor R-638, and a d cost (B-6potential is applied via resistor R- 637 to amplifier U-fi. Servo M200will thusly rotate until these two inputs are equal in magnitude andopposite in polarity, at which time the shaft position of servo M-200will be a measure of the angle (}85 and the servo will have solvedequation (30).

The h potential on the arm of potentiometer R-601 is applied viaresistor R613 to feedback amplifier U-601. The h potential on the arm ofpotentiometer R-607 is inverted in phase by amplifier U602 and appliedto amplifier U-601 via resistor R414. The output potential fromamplifier U-601 is modified in accordance With reference altitude h bypotentiometer R-605 and applied to the input circuit of amplifier U-601so that the resultant potential output from amplifier U-601 isproportional to amplifier U-6l6 to position servo M-500. A conventionalfollow-up potentiometer R 648 is provided on the shaft of servo M500 toprovide re-balancing voltage.

The lateral displacement or d potential on the arm of potentiometer R611is applied via resistor R622 to amplifier U-606. The output potential ofamplifier U- 606 is modified in accordance with simulated altitude h bypotentiometer R-609 and fed into amplifier U406 so that the resultantoutput potential of amplifier U-606 is proportional to d/h Thispotential is applied via resistor R652 and amplifier U-617 to positionservo M-600. Follow-up potentiometer R-649 provides re-balancingpotential for servo M600 in conventional manner. Servo M-500 shifts thedistorted picture vertically and servo 15 M-600 shifts the distortedpicture laterally as explained in connection with FIG. 8 to establishthe projected image in the right place on the viewing surface.

Shown in FIG. 7 is a perspective view of a specific embodiment of thedistorting means of the invention. The distorting means comprises a pairof mutually perpendicular anamorphic distorting elements attached todistort the image from a conventional motion picture projector. Axiallyaligned with the projector optical axis and fitted over the projectionlens L of projector PR is a cylindrical bearing hub 101 which is rigidlymounted on the projector case as by means of bolts 102, 103. Around theperiphery of hub 101 a bearing portion 104 is provided to accommodate acooperating groove in the base portion of lens barrel 105, which isthereby rotatably secured to the projector. Gear teeth may be providedaround lens barrel 105 as shown at 106. Bevel gear 107 meshes with theteeth on lens barrel 105, so that rotation of motor M100 serves torotate lens barrel 105 about the optical syst m axis. The base portionof lens barrel 105 carries motors M-300 and M 100, which are likewisemoved bodily around the system optical axis upon rotation of motorM-l00. Pinion 108 meshes with a toothed surface 109 extending around theperiphery of sleeve 110, so that rotation of motor M-300 rotates sleeve110 around the lens barrel 105. Sleeve 110 is provided with twonon-linear cam slots 111, 113 which engage pins 113, 114. Pins 113 and114 extend through longitudinal slots out in lens barrel 105 so thatpins 113 and 114 are constrained against rotation about the optical axisbut move parallel to the system optical axis upon rotation of sleeve110. Pins 113 and 114 are rigidly aflixed to the mounting rings 115 and116, respectively, of positive cylindrical lenses LA2 and L-A1, so thatlongitudinal movement of pins 113 and 114 moves lenses LA-l and LA-Zalong the system axis, the lens mounting rings 115 and 116 being guidedas by means of keyways 117, 118. Also provided within lens barrel 105 isa negative cylindrical lens L-AN which is fixedly mounted within lensbarrel 105. Thus it may be seen that rotation of sleeve 110 by means ofmotor M300 will serve to position positive cylindrical lenses LA-1 andLA2 with relation to negative cylindrical lens L-AN. Lenses LA-l, LA-2and LAN each may be seen to be cylindrical in a vertical direction asviewed in FIG. 7.

Motor M-400 positions sleeve .120 about lens barrel 105 in the samemanner that motor M-300 positions sleeve 110. Pins 123 and 124 aretranslated longitudinally by cam slots 121 and 122, respectively,axially moving positive cylindrical lenses LB-l and LB2 with respect tofixed negative cylindrical lens L-BN. Lenses LA-l, LA-2 and L-ANcomprise a first variable anamorphic means, and lenses LB-l, LB2 andL-BN comprise a second variable anamorphic means. Lenses LB-l, LB2 andL-BN are each cylindrical in a horizontal direction as viewed in FIG. 7,and hence it may be seen that the two anamorphic means areperpendicularly disposed. That appropriate axial movement of a pair ofpositive cylindrical lenses with respect to a fixed negative cylindricallens will provide variable magnification in one direction withoutde-focus is explained in detail in my abovementioned copendingapplication and need not be repeated herein. The invention is notlimited, however, to the precise form of anamorphic means hereinemployed (two positive and one negative lenses), and it will be readilyapparent to those skilled in the art that pairs of perpendicularlydisposed anamorphic means using other lens element combination may besubstituted for the precise form of variable anamorphic means shownwithout departing from the invention. As will be further explainedbelow, rotation of motor M-100 serves to rotate the anamorphic pairdistorting means through the angle {3 required to simulate a desiredviewpoint displacement, motor M-300 serves to position the lenses LA-1and LA2 to provide the first anamorphic power M required to simulate thedesired viewpoint displacement, and motor M-400 serves to positionlenses LBl and LB2 to provide the second anamorphic power M required tosimulate the desired viewpoint displacement. The positioning of motorsM-100, M300 and M-400 will distort the image from projector PR so as toprovide a distorted image having the correct shape to simulate the viewas seen from the desired viewpoint, but it will be further necessary torotate the distorted image through an angle of ,8-6 n order thatoriginally horizontal objects remain horizontal in the distortedpicture, and in systems using images taken with the camera axis belowthe horizon, to shift the distorted image vertically and laterally.These three further corrections may be made by rotating the entireprojector system (including the anamorphic distorting pair) through theangle 5-6,, and by displacing the original image in the projectorvertically and laterally with respect to the anamorphic distorting pair.In providing a visual display for use with grounded trainers, I usuallyprefer to rotate the entire projector system relative to the observerthrough the (fit-6 angle, and to move the distorted image vertically andlaterally on the screen by appropriately rotating the entire projector,as is shown in detail in FIG. 11.

Shown in FIG. 9 is an exemplary electrical control system which may beutilized to interconnect the previously described optical system to aconventional grounded trainer so as to provide realistic visualdisplays. Modern grounded aircraft trainers or simulators are commonlyprovided with integrating or velocity servos responsive to potentialsrepresenting components of simulated ground speed in two directions,usually termed northerly and easterly, and which servos integrate thecomponent potentials with respect to time, producing as shaft outputsquantities representing simulated aircraft distances with respect to areference point on the ground. A recording pen is commonly actuated bysuch shaft outputs to trace the cause of simulated flight on a map forobservation by the instructor. If it is desired to produce a realisticvisual display during both simulated takeoffs and landings a swell assimulated flight in the air, and if wind conditions are also to besimulated, it is important that the simulated aircraft distancequantities derived be accurate measures of the aircraft location withrespect to a fixed point during takeoffs and landings as well asairborne flight. To provide such quantities, the invention may be used,for example, in conjunction with the computer apparatus disclosed inapplication Serial No. 477,741 filed December 27, 1954 by Laurence E.Fogarty for Aircraft Trainer Apparatus, which application is assigned tothe same assignee as the present invention, and which applicationdiscloses means for providing the desired quantities during all phasesof a simulated flight, while realistically taking into account theeffects of wind. In the apparatus of FIG. 9 servos M-102 and M-101 maycomprise such integrating servos. Servo M-102, the position of whichrepresents the distance of the simulated aircraft north of the referencepoint, positions the arm of potentiometer R-200, the winding of which isexcited with a constant excitation from the conventional groundedtrainer computer power supply, deriving a potential commensurate withmiles north of the simulated aircraft from the reference point, whichpotential is applied via resistor R208 to summing amplifier U-200. ServoM-101 and potentiometer R-201 similarly derive a miles east potentialwhich is applied via resistor R-210 to amplifier U201. PotentiometersR-202 and R-203 are provided with control knobs manually positionable bythe instructor so that the arms of potentiometers R-202 and R-203 may bepositioned in accordance with a desired northerly distance and a desiredeasterly distance, respectively, of a simulated airport from thereference point. The windings of potentiometers R-202 and R203 areexcited from the computer power supply with constant Potentials ha ingan instantaneous polarity opposlte to those potentials applied to excitepotentiometers R-200 and R-201. Since the station location potentialsfrom potentiometers R-202 and R-203 are applied (via resistors R-209 andR-211) to amplifiers U-200 and U-201, in opposite sense to the aircraftlocation potentials, it will be seen that the difference outputpotentials from the amplifiers will represent northerly and easterlydistances of the instantaneous flight position of the simulated aircraftfrom the selected airport location. These difference potentials are eachapplied individually to one rotor coil 'of a conventional inductionresolver T-l. The resultant voltage induced in stator coil L of resolverT-1 is applied to a conventional servo M-103, the output shaft of whichrotates the rotor coils until minimum voltage is induced in coil L Thiscauses servo M-103 to provide an output shaft position representing theangle between the bearing from simulated aircraft to simulated airportand a north or east reference direction. At balance the potentialinduced in resolver stator coil L will be a maximum, and will beproportional to the vector sum of the potentials applied to the rotor,representing in magnitude the resultant distance between the simulatedaircraft I and the selected simulated airport site. This resultantdistance potential is applied via resistor R-212 to the control circuitof a polarity-sensitive relay means PSR-l. Potentiometer R-204 isexcited by a constant potential of opposite sense, and its arm ispositioned by the instructor in accordance with the maximum distance atwhich it is desired that the trainer be provided with a visual picture.A potential proportional to such distance is thereby applied topolarity-sensitive relay means PSR-l via resistor R-213. When thesimulated aircraft is at a distance exceeding that selected bypotentiometer R-206, the potential applied to relay PSR-l via resistorR-212 will exceed that applied through resistor R-213, and contact a ofrelay PSR-l will remain open. When simulated aircraft distance becomesless then the distance selected by the setting of potentiometer R-204,the polarity of the resultant potential applied to relay PSR-l willreverse, causing relay PSR-l to close its contact a.

The conventional grounded trainer altitude servo M- 1100 positions thearm of potentiometer R-207, applying a potential commensurate withinstantaneous altitude of 'simiulated flight to polarity sensitive relaymeans PSR-Z and PSR-3 via resistors R-215 and R-217, respectively.Provided for manual setting by the instructor are potentiometers R-205and R-206, which may be set to correspond respectively to upper andlower limits of the allowable area within which the student must fly thegrounded trainer to be provided with a visual presentation. For example,potentiometers R-205 and R-206 may be set in accordance with the upperand lower limits of a conventional instrument landing system radiationpattern, so that the student must fly within the radiation pattern inorder to obtain a visual presentation. Potentiometers R-205 and R-206may be provided with tangent function windings and excited with thetrainer-to-airport dis- 'tance potential from coil L to resolver T-l, sothat the output potentials appearing on the arms of potentlometers R-205and R-206 represent the maximum and minimum altitudes at which thesimulated aircraft must be situated at any particular distance from theairport if a visual image is to be presented. The maximum allowablealtitude potential from potentiometer R-205 is applied via resistorR-214 to relay PSR-2, and the minimum allowable altitude potential frompotentiometer R-206 is applied to relay PSR-3. As the altitude ofsimulated flight exists between the upper and lower limits selected bypotentiometer-s R-205 and R-206, the a contacts of both relays PSR-2 andPSR-3 will be closed. If the simulated flight altitude decreases belowthat selected by potentiometer R-206, the polarity of the resultantpotential applied to relay PSR-3 will reverse, opening contact a ofrelay PSR-3. Conversely, if simulated flight altitude increases so as toexceed that selected by pothe student.

tentiomete r R-205, the polarity of the resultant potential supplied torelay PSR-2 will reverse, opening contact a of relay PSR-2. Thus acomplete circuit exists through the contacts of relays PSR-l, PSR-2 andPSR-S only when the simulated aircraft is maintained withinallowdifferential 210. Applied as another input to differential 210 is ashaft rotation selected by the instructor in accordance with the desiredheading of the runway at the simulated airport. The runway heading inputshaft is manually positoned by the instructor and retained in posi--tion by friction means indicated generally as 211. Thus it will be seenthat the position of output shaft 212 of differential 210 will becommensurate with the difference between aircraft-to-station bearing andrunway heading. Shaft 212 positions cam 213, which operates switch8-203. Cam 213 is provided with a rise along a portion of its peripherycorresponding to twice an arbitrary maximum allowable amount thattrainer to station hearing may be allowed to deviate from runwayheading. Cam 213 is shown in a position corresponding to directalignment of the aircraft to station bearing with the runway heading,the cam follower of switch 5-203 being centered on the cam rise. If thesimulated aircraft approaches the simulated airport at such a bearingthat cam 213 no longer closes switch S-203, no visual display will bepresented to If a constant potential is applied to terminal 200, it willnow be understood from the above explanation that the potential will beapplied via contact a of relay PSR-l if the simulated aircraft is withinsuitable distance of the simulated airport, via contacts a of relaysPSR-2 and PSR-3 if the simulated aircraft is 'within suitable altitudelimits, via switch 3-203 if the simulated aircraft approaches theairport from a suitable direction, via contact b of switch 8-202 and vianormally-closed switch 5-204 and intensity rheostat R-229 to projectorlamp 214. If the student operates the simulated controls so as to exceedany of the allowable limits, projection lamp 214 will be de-energized,and no picture will be cast upon the screen.

Switch S-201 applies a reference altitude potential to positionreference altitude servo M-1000, a conventional grounded trainerposition servo (which is equipped with a conventional follow-uppotentiometer not shown) and which is used for computing as explainedabove in con- 'nection with FIG. 6. The reference altitude potential maybe derived in a number of ways, and two exemplary arrangements are shownin FIG. 9 for deriving such potential. The upper contact of switch S-201is supplied with a reference altitude potential may be derived in anumber of ways, and two exemplary arrangements are shown in FIG. 9 forderiving such potential. The upper contact of switch S-201 is suppliedwith a reference altitude potential from aplifier U-202 which is derivedas will be explained in connection with FIG. 13. A reference altitudepotential derived from indicia coded on the film is provided on thelower contact of switch 8-201. A conventional photocell pickup X-1 onthe projector derives pulses periodically from indicia coded as blackand white areas along the soun track of the film.

These pulses are amplified by amplifier U-'206 and applied to operatedigital voltage generating means shown as comprising a pair of simplestepping switches K-202 and K-203. Successive pulses applied to the coilof stepping switch K-202 as the simulated aircraft approaches theairport site translates its selector arm counterclockwise as viewed inFIG. 9, applying lesser amounts of voltage through resistor R-220 toamplifier U-204. When the selector arm of switch K-202 arrives at itsfurthest 1 9 counterclockwise position, contact b of switch K-202 isswitched so that the output of amplifier U-206 is then applied to thecoil of identical stepping relay K203. Further pulses from amplifierU-206 then translate the selector of switch K-203 counterclockwise,applying lesser voltages to amplifier U-204 via resistor R-221. Thestepping switches utilized may have many more contact positions thanshown, so that the reference altitude potential is changed in very fineincrements, and many more than two stepping switches may be cascaded. Itwill be apparent to those skilled in the art that the altitude at whicheach picture was taken may be coded on the film 'in analogue fashionrather than digital, if desired, al-

though digital coding is preferred because of its inherent greateraccuracy. Analogue coding could consist, for example, of a frequencyproportional to altitude, and a. conventional frequency discriminatorcircuit (not shown) connected to the output of amplifier U-206 wouldproduce a potential proportional to reference altitude.

The aircraft-to-airport distance or range potential on coil L ofresolver T-l is also applied via scaling resistance R231 to amplifierU-202. A potential proportional to simulated aircraft altitude isapplied via scaling resistor R230 to summing amplifier U-202. The outputof summing amplifier U-202 represents the sum of the applied signals,and as will be fully explained in connection with FIG. 13, iscommensurate with a corrected or modified range between the aircraft andairport. The corrected range output potential is applied to excite thewindings of tangent potentiometer R-222, which is shown schematicallyfor sake of clarity as a simple potentiometer, but which may actuallycomprise two tangent potentiometers so as to be capable of 360 degreerotation. The arm of potentiometer R-222 is positioned by the outputshaft 212 of differential 210 in accordance with angular difference between trainer-to-station bearing and runway heading, so that thepotential appearing on the arm of potentiometer R-222 is proportional tothe lateral displacement of the simulated aircraft from the airportrunway centerline extended. The lateral displacement potential isapplied via resistor R-223 to position lateral displacement or d servoM4200, which is provided with a conventional follow-up potentiometerR224. The output shaft of servo M-1200 positions potentiometers asdescribed above in connection with FIG. 6.

It will 'be seen that whenever the simulated aircraft comes within therange set by potentiometer R204, that closure of contact a of relayPSR-1 will cause energization of relay K-201, closing contact a of relayK-201 and applying the aircraft-to-airport corrected range potentialfrom amplifier U-202 via contact "a of switch 8-202 and resistor R-227to film drive servo M-205. The film drive servomotor is a conventionalposition servo, so that film will be fed through the projector at therate at which the simulated aircraft approaches the simulated airport,and each particular field frame will represent a particular distancefrom the airport. It may be noted that the film drive will start as soonas the simulated aircraft reaches a minimum distance from the simulatedairport regardless of whether the simulated aircraft is then withinallowable altitude and direction limits. This serves to insure that thecorrect film frame will be in the projector immediately no matter whenthe simulated aircraft comes within the allowable altitude and directionlimits.

After a simulated landing has been made and most of the film has beenrun, the instructor may reload the projector by moving switch 8-202 toits lower position. This applies a potential commensurate with themaximum visual pickup distance selected by potentiometer R-204 to thefilm drive servo M-205 via contact a of switch 8-202, causing reversefeed of the film until it is again located in its original position,with the frame then in the projector corresponding to the scenephotographed at such maximum distance. Contact b of switch -202deenergizes projection light source 214 while the projector is being runin reverse. Lower contact c of switch S 202 applies voltage to the coilof stepping switch K-202 through self-interrupting contact a of switchK402 causing the switch to rotate counterclockwise rapidly until theswitch arrives in its last position, at which time closure of contact 0of switch K-202 shorts self-interrupting contact a, halting rotation ofswitch K-202. Return of switch S202 to its upper position will thende-energize the coilof the stepping switch, allowing it to advance onemore position counterclockwise to its original position. Identicalswitch K-203 and any further stepping switches may be connectedsimilarly. By momentarily opening switch S-204, and by varying thesetting of rheostat R-220 the instructor may cause temporary loss of thepicture and may simulate varying visibility conditions. It will beapparent that simulation of takeoifs as well as landings may be providedby use of films taken during reference takeoifs. In such systems theprojected picture may be removed from the screen by de-energizing theprojection lamp after the simulated aircraft has moved an arbitrarydistance.

If the object utilized to project images of the ground area comprises amotion picture film taken during an actual reference flight as mentionedabove, it may be desirable to provide a reference altitude potentialwhich decreases non-linearly as the simulated aircraft approaches theairport, since it is practically impossible in many aircraft to maintaina glide path of constant slope down to ground altitude, it beingnecessary to level off shortly before touchdown. Hence it may benecessary to take the pictures along a non-linear glide, path. Thereference altitude potential may be made to change non-linearly withrepsect to aircraft-to-airport distance by means of a variety of readilyapparent techniques. For example, a non-linear resistance or otherdevice. may be inserted between amplifier U-202 and the upper contactwith switch 8-201. Using the means shown to derive the referencealtitude potential from indicia coded on the film, it will be apparentthat code marks may be spaced at increasing intervals on the film soundtrack to provide a more slowly decreasing reference altitude potentialalong that portion of the film projected during the leveling off periodof flight. Being derived with respect to displacement from a straightline coincident with the simulated airport runway centerline, thelateral displacement signal derived by the apparatus of FIG. 9 presumesthat the pictures on the film were either taken during a flight down astraight centerline or were distorted by use on the camera of opticalapparatus similar to that of FIG. 7 to have the appearance of beingtaken along the centerline. While it is usually possible to fly anaircraft along a substantially straight line, and while it is easy tomove a camera in a straight line in relation to a model ground scene,indicia may be coded on the sound of the film indicating anydisplacement of the camera from the centerline during the taking of thepictures. A lateral displacement signal commensurate in magnitude andpolarity with the deviation of the camera in distance and direction froma straight line may be derived by apparatus similar to that used toderive the altitude reference signal from the film, and such lateraldisplacement signal may be combined in a summing amplifier (not shown)with the lateral displacement potential from potentiometer R- 222 tocorrect the position of d servo M-1200.

It may be noted that a change in [3 of 180 degrees results in no changein the projected image, since each of the variable ana'morphosers issymmetrical about the optical axis. However, if the path of simulatedflight passes through the reference path, or passes near the referencepath between points situated in different quadrants of a circle drawnaround the reference path, the value of 5 required to effect the desireddistortion may change rapidly from a plus angle to a minus angle, whichmight require 3 servo M- to invert the distorting system very quickly.Since the phenomenon may be noticeable, it is desirable to locate thereference path along a line which the simulated aircraft does notregularly fly. F or example, if the student is expected to make alanding approximately along the guide path of a conventional instrumentlanding system, it is desirable to locate the reference path away fromthe guide path beam line, so that the simulated aircraft will not berepeatedly passing through the reference path.

As shown schematically in FIG. 9 servo M-100 serves to rotate bothanamorphic distorting means, servo M-300' serves to vary themagnification of the first anamorphic means by rotating sleeve 110 andservo M-400 serves to vary the magnification of the second anamorphicmeans by rotating sleeve 120, all as shown and explained in connectionwith FIGS. 6 and 7. As shown schematically in FIG. 9 servo M-200 servesto roll or bank the entire projection apparatus to maintain the horizonlevel, servo M-500 serves to pitch the entire projection apparatus toprovide the required amount of vertical shift, and servo M-600 serves toyaw or turn the entire projection apparatus to provide the requiredamount of lateral shift, as explained above in connection with FIGS. 1,6 and 8.

Shown in FIG. 12 are portions of an alternative embodiment of theinvention in which cooperatively related electrical distorting means areutilized to provide a proper visual display. The projector PR may bemounted upon the same type of tilting mechanism as that shown in FIG.11, with the projected image focused upon the lens of conventionaltelevision camera 703. The camera or pickup is provided in conventionalmanner with sweep potentials from vertical and horizontal oscillators orsweep generators 700 and 701, which cause the camera tube to scan theimage received from projector PR, providing in conventional manner uponconductors 711, 712 a video signal containing picture information. Thevideo signal is applied via amplifiers (not shown) if desired, betweenthe grid and cathode of a conventional projection cathode ray tube CRT.The projection cathode ray tube CRT is provided in conventional mannerwith filament and anode voltages 'by means not shown so that a beammodulated in accordance with the picture information is cast upon theface of CRT. It will be seen that if sweep potentials corresponding tothose applied to camera 703 were applied to deflection coils L-X and L-Yof CRT, that a picture substantially duplicating that projected byprojector PR would appear on the face of CRT. The sweep potentialsutilized to drive the camera tube are modified, however, in accordancewith the positions of servo M-300 and M-400 to provide a picture on CRTwhich may be relatively expanded in one dimension and relativelycompressed in a perpendicular second dimension. Deflection coils LX andL-Y encircle the neck of tube CRT in conventional manner, but ratherthan being mounted fixedly to the tube, the coils may be rigidlyattached to a fiber, micarta or other non-magnetic ring gear 708, whichencircles the neck of tube CRT and serves to rotate coils L-X and L-Yaround the beam axis in the same manner deflection coils are rotated inconventional plan position indicator radar scopes. Each deflection coilis provided with a pair of slip rings (such as ring 705) which areengaged by wipers (such as 706). Deflection coils L-X and L-Y may beaffixed to ring gear 708 with their axes of deflection perpendicular toeach other.

The size of the picture projected upon CRT depends upon the range (peakto peak amplitude) of the sweep potentials applied to the deflectioncoils, and hence the amplitudes of such potentials are controlled inaccordance with the desired magnification along both of theperpendicular axes of the picture. Amplifiers U-703 and U- 704 representconventional sweep potential power amplifiers utilized to provide therequired trapezoidal Waveform currents used in electromagneticdeflection systems. With no signal input to amplifiers U703 and U-704the current applied to coils L'X and L-Y may be adjusted to maintain thebeam of CRT centered on the face. The vertical sweep potential fromsweep generator 701 is applied through isolating means U-701 (such as afeedback amplifier or cathode follower) to excite the winding ofpotentiometer R-701. The arm of potentiometer R701 is positioned by M,servo M-300, thereby applying an input potential to amplifier U-703corresponding to the vertical sweep potential of the camera tubemodified by the desired magnification (M,,) of the picture in itsdimension determined by deflection coil LY. Servo M400 and potentiometerR-702 control the size of the picture along its dimension determined bycoil L-X in similar manner.

If the projector tilting mechanism 30 is rolled in in accordance withthe angle B by servomotor M100, it will be seen that the video signalsderived on conductors 711, 712 are derived with reference to a sweepsystem having its horizontal and vertical sweeps each acting parallel toone of the axes of magnification M M of the image. For example, ifprojector PR is rolled 10 degrees from a vertical position by servoM-100, the video signals derived by camera 703 would produce a picturein which the vertical sweep direction differed by ten degrees. Byrotating projector PR relative to camera 703 through the angle ,8, thevertical and horizontal sweep directions of the picture derived as avideo signal are made to correspond to the perpendicular axes ofmagnification, M and M Then by varying the range of the sweep potentialsas described above, the size of the resulting picture is controlled. Theresulting picture, however, must be continuously rotated through theangle 6 in order to maintain things parallel to the horizon level on theface of the cathode ray tube. As indicated schematically in FIG. 12 suchangular orientation may be effected by rotating the deflection coilsabout the scope by means of bevel gear 709. The re-orientation' may alsobe eifected by rotating the entire cathode ray tube and using aconventional cathode ray tube in which the deflection coils are notallowed to rotate about the axis of the signal beam. If 5 servo M- and5-5;, servo M-200 are applied as inputs to an ordinary me chanicaldifferential 710, an output shaft position to operate gear 709 throughthe angle 6 is available. It will be apparent to those skilled in theart that in constructing a system in accordance with this embodiment ofthe invention, that a 5,, servo may be provided in place of the (/35,,)servo to drive gear 709 or to rotate the entire cathode ray tubedirectly by solving for 6 in accordance with well known analoguecomputer technique. By solution of the simultaneous equations givenabove, the angle 5 may be fonnd to be expressible as:

The image on the face of CRT is focused in convenmay be used to operateeither distorting means. Although shown) to be viewed by the student. Itwill be understood that the electrical distorting means shown in FIG. 12may be substituted for the optical distoring means of FIG. 7 and thesame computing and control apparatus may be used to operate eitherdistorting means. Although I have shown electromagnetic deflection meansin FIG. 12, and although I prefer to employ such means rather thanelectrostatic means due to the difliculty in constructing rotatableelectrostatic deflection means, those skilled in the art will recognizethe possibility of substituting electrostatic deflection means withoutdeparting from the invention. In such systems rotation of the image maybe accomplished by applying the deflection potentials to a resolverpositioned in accordance with the angle 5 in a manner similar to thatsometimes used for rotating tan 2 6 objects on electrostatic planposition indicator radar screens. And although I have shown a distortingsystem using a uniform sweep on the camera tube and a modified sweep onthe projection cathode ray tube, it will become apparent that it is therelative amplitudes of the two sweep systems which cause the requireddistortion, and hence the camera tube and cathode ray tube sweepdeflection means may be interchanged without departing from theinvention. Such an arrangement requires, however, that the sweepamplitude modifying potentiometers be driven in accordance with thereciprocals of M and M and hence in constructing such an embodiment itis preferable to connect servos M-300 and M-40t) so as to provide shaftoutputs commensurate with the reciprocals of the desired magnifications.The required modifications of the circuit of FIG. 6 to effect suchoperation will be readily apparent to those skilled in the analoguecomputer and flight simulator art and need not be set forth herein.

The anamorphic distortion system shown and described in the precedingfigures simulates viewpoint displacement within a single plane. Bothactual and simulated aircraft rarely, if ever, move within a singleplane. If a series of successive objects having the appearance of anarea as viewed from succession of points along a reference path isprovided, selection of one of said objects in accordance with the pointit represents and proper distortion of an image of the selected objectin accordance with the displacement between said point and a simulatedviewpoint may provide a realistic visual display. If said objects aresuccessively projected with controlled amounts of distortion, a motionpicture scene simulating motion along a selected path may be provided.In determining the particular object to use to project a scene during aparticular point along the selected path, it is often desirable toconsider the displacement of the viewpoint in terms of the referencepath slope and the angle at which the objects represent the areasviewed. If a series of successive objects having the appearance of anarea as viewed from a succession of points along a reference path areprovided, by properly selecting the proper one of such objects inaccordance with reference path angle and camera angle as well asdistance along said path, and by properly distorting an image of saidselected object a more realistic display may be presented. Referring toFIG. 13 there is shown diagrammatically in elevation a reference flightpath B-B along which an aircraft may be flown while motion pictures aremade of the scenes visible through the windshield of the aircraft, oralternatively, a camera may be moved along such a path relative to aminiature ground scene. Each frame of the motion picture will be seen torepresent the area as viewed at a particular point along the referencepath, F F F et cetera represent individual film frames taken atsuccessive points along a reference path which slopes at an angle (X111to the horizontal, and each frame may be taken and later projected at anangle 6 from the vertical as mentioned above in connection with FIG. 8.The film frame planes are indicated with an exaggerated separationbetween them for sake of clarity. In ordinary embodiments of theinvention, the camera utilized when taking pictures along the referencepath may be driven at a rate of 24 frames per second, for example, whilethe aircraft travels toward the grounded reference point at a speed of120 feet per second, for example. A frame will be taken then,approximately every five feet.

Assume that the simulated aircraft is located at point P. In order toprovide the proper visual display, one need merely project an image offrame P with no distor- .tion. If distortion is provided the scenesprojected will simulate what is seen from various viewpoints locatedwithin .the plane of frame F Since the simulated aircraft will be at aninstantaneous ground range R from the ground reference point C at theairport site, the film drive servo M-ZOS should position frame F in theprojector.

But now assume that rather than being located on the reference path,that the simulated aircraft has deviated to, for example, point P belowpoint P. It will be seen that the desired scene may not be obtainedperfectly accurately by projecting a distorted image of frame F but thatan image of frame F should be projected. It will be seen that in systemsutilizing a reference path of small slope and a small camera angle(camera and projector axes nearly horizontal), that the displacedviewponit P will lie on or very near the plane of the fihn framecorresponding to the instantaneous distance to the airport or touchdownpoint, but that as the slope of the reference path increases or thecamera angle utilized is increased, the number of frames between theframe corresponding to the instantaneous ground range and the frame inthe plane of which the displaced viewpoint is located will increase fora given amount of displacement of the simulated aircraft from referencealtitude. It will be apparent that the inaccuracy of the projected imagewill be a function of the number of frames between the framecorresponding to instantaneous ground range and the frame having thesimulated viewpoint in its plane, so that in certain embodiments of theinvention it becomes desirable to correct such inaccuracy.

In order to project frame F when the simulated aircraft is at point l, aground range R from the airport reference point, the range signalapplied to the film drive servo M-205 should be derived in the correctmagnitude to position frame F into the projector. It will be seen thatthis may be accomplished by decreasing the range potential applied toservo M-ZOS by an amount propor- Expression (41) indicates that if thereference path elevation angle i1 1 and the film plane or camera angle 6are maintained constant, that the corrected potential required toposition film drive servo M205 may be obtained by adding a potentialproportional to simulated aircraft altitude to a potential proportionalto simulated ground range if suitable scaling is provided. As shown inFIG. 9, the correction potential proportional to simulated altitude isapplied from the wiper of altitude responsive potentiometer R-2ti7 torange summing amplifier U-202 via scaling resistor R 230, and adds withthe potential applied from coil L of resolver T1 through resistor R 231to provide a corrected range potential at the output of amplifier U202.Resistor R-231 is chosen to apply a 1+tan 6 tan (1F scaling constant tothe ground range potential from resolver T 1, and resistor R230 ischosen to apply a scaling constant of tan 6 1+tan 6 tan u 25 to thepotential applied from altitude responsive potentiometer R-207. FromFIG. 13 reference altitude h, of frame F; may be seen to be directlyproportional to the corrected range potential R times, a constant; or:

tan a R-l-h tan e cos 6 1+tan 6 tan (1F Thus it may be seen that byproviding suitable scaling resistance between amplifier U-202 and theupper contact of switch S-201, a potential commensurate with h, willappear on the upper contact. If films taken at a variety of cameraangles or along glide paths of different slopes are to be utilized withthe apparatus of FIG. 9, resistances R230 and R-231 may be made variableto vary the scale factors. When the selector arm of switch S201 is inits upper position, the signal applied to reference altitude servo M1000is automatically corrected to the frame F; reference altitude, since thepotentiometers R-205 and R-206 utilized for deriving the referencealtitude potential are excited by the corrected range potential outputfrom summing amplifier U-202. Hence by governing the projector filmdrive in accordance with simulated altitude while taking into accountthe reference path slope and the camera angle, the proper film frame maybe projected at the proper instant, and the distortion computing systemmay be provided with the required input quantities. It will be apparentthat since corrected range R is a function of both actual ground range Rand altitude h that when simulated aircraft altitude exceeds referencepath altitude, that a converse operation will occur, and a correctedrange potential of the magnitude required to make the film drive lagproperly will be derived, -so that the particular film frame located inthe projector at any instant will have the simulated aircraft viewpointlocated within or nearly within the plane in which the film was taken.If the reference altitude signal is derived from indicia coded on thefilm rather than from simulated aircraft range (i.e., switch 8-201 ismoved to its lower contact) no altitude correction of the rangepotential is necessary for given camera and reference path angles, sincethe film coding may be spaced so as to insure that the film frame beingprojected at any instant derives the correct reference altitudepotential.

While I have illustrated the invention as utilized in conjunction withgrounded aircraft training apparatus, it will be readily apparent tothose skilled in the art that it is applicable as well to other trainingapparatus such as automobile trainers, and as a matter of fact, its useis not limited to training devices. The invention may find use whereverit is necessary or desirable to alter the apparent perspective of animage to make a scene appear as if it is being perceived from adilferent viewpoint. Certain special effects utilized in the productionof motion pictures for entertainment purposes may be made by use of theinvention, since the ability of the invention to alter the apparentperspective of images allows realistic simulation of scenes as viewedfrom viewpoints where it may be impossible or impractical to position acamera. Furthermore, while I have illustrated the invention as usingmotion picture film frames, it will be immediately apparent that theinvention is applicable as Well to the alteration of the apparentperspective of still pictures, and that as well as images from filmtransparencies, that images from other transparencies and also reflectedimages may be utilized with the invention.

The details of the specific type of variable power anamorphosers are notessential features of the invention, and those skilled in the art mayfind it desirable in some embodiments of the invention to utilizevariable power anamorphosers constructed of different combinations oflens elements. It will also be apparent to those skilled in the art thatthe elements of the two anamorphosers may be interleaved in someembodiments of the invention. It will be apparent to those skilled inthe art that the term variable power anamorphoser is meant to embraceany lens combination having a variable power in a first direction and afixed power in a perpendicular second direction, and that the fixedpower need not be unity. Those skilled in the art will also recognizethat the plane of a viewpoint is the plane passing through the viewpointwhich is perpendicular to the line of sight from the viewpoint to thescene observed.

It will thus be seen that the objects set forth above, among those madeapparent from the preceding description, are efiiciently attained. Sincecertain changes may be made in carrying out the above method and in theconstructions set forth without departing from the scope of theinvention, it is intended that all matter contained in the abovedescription or shown in the accompanying drawing shall be interpreted asillustrative and not in a limiting sense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween.

Having described my invention, what I claim as new and desire to secureby Letters Patent is:

1. Apparatus for altering the apparent perspective of an image of anobject having the appearance of an area as viewed from a referenceviewpoint located at a reference altitude h, to provide an image havingthe appearance of said area as viewed from a selected viewpoint locatedat a selected altitude h and displaced laterally in the plane of saidreference viewpoint a distance d from said reference viewpointcomprising in com. bination scanning means having a pair ofperpendicularly disposed sweep means for scanning said object to providevideo signals, a cathode ray tube connected to receive said videosignals to produce a beam modulated in accordance with said signals,said cathode ray tube having a pair of perpendicularly disposed beamdeflection means, means for providing an axial relative rotation betweensaid object and said scanning means through an angle ,8 determinablefrom the expression:

Where the ratio M, between M and M is determinable from the followingexpression:

d2 h1 h2 +r=0 2 1 2 2 1:i

and means for axially rotating the image produced by said cathode raytube through an angle 5,, determinable from the following expression:

sin 2d:

2. Apparatus according to claim 1 in which the last recited meanscomprises means for axially rotating said cathode ray tube beamdeflection means about said cathode ray tube beam.

3. Apparatus according to claim 1 in which the last recited meanscomprises means for axially rotating said cathode ray tube together withsaid cathode ray tube beam deflection means.

tan 25 (References on following page)

1. APPARATUS FOR ALTERING THE APPARENT PERSPECTIVE OF AN IMAGE OF ANOBJECT HAVING THE APPEARANCE OF AN AREA AS VIEWED FROM A REFERENCEVIEWPOINT LOCATED AT A REFERENCE ALTITUDE H1 TO PROVIDE AN IMAGE HAVINGTHE APPEARANCE OF SAID AREA AS VIEWED FROM A SELECTED VIEWPOINT LOCATEDAT A SELECTED ALTITUDE H2 AND DISPLACED LATERALLY IN THE PLANE OF SAIDREFERENCE VIEWPOINT A DISTANCE D FROM SAID REFERENCE VIEWPOINTCOMPRISING A COMBINATION SCANNING MEANS HAVING A PAIR OF PERPENDICULARLYDISPOSED SWEEP MEANS FOR SCANNING SAID OBJECT TO PROVIDE VIDEO SIGNALS,A CATHODE RAY TUBE CONNECTED TO RECEIVE SAID VIDEO SIGNALS TO PRODUCE ABEAM MODULATED IN ACCORDANCE WITH SAID SIGNALS, SAID CATHODE RAY TUBEHAVING A PAIR OF PERPENDICULARLY DISPOSED BEAM DEFLECTION MEANS, MEANSFOR PROVIDING AN AXIAL RELATIVE ROTATION BETWEEN SAID OBJECT AND SAIDSCANNING MEANS THROUGH AN ANGLE B DETERMINABLE FROM THE EXPRESSION: